How to duplicate Weights to different Bones WITHOUT painting?
If you have the bones named as Leander suggests (i.e., a left and right side naming convention and all needed bones in place), you can delete one half of your model (the half with the weights you want to copy), and then add a mirror modifier. Move the bones on the mirrored side around to see if it's working correctly, then apply the modifier. The only time this won't work is if you have shape keys on the model, since you can't easily remove modifiers on a model with shape keys.